# Role of pair-vibrational correlations in forming the odd-even mass difference

## TL;DR

This paper extends the RPA-amended Nilsson-Strutinskij method to odd-A nuclei, showing that pair-vibrational correlations significantly influence odd-even mass differences, especially in light nuclei, providing a more accurate nuclear binding energy model.

## Contribution

It introduces the application of RPA corrections to odd-A nuclei within the nuclear binding energy calculation, highlighting their significant impact on odd-even mass differences.

## Key findings

- RPA correction accounts for most of the odd-even mass difference in light nuclei.
- The size and sign of RPA contributions vary across nuclei.
- RPA corrections improve the accuracy of nuclear mass models.

## Abstract

In the random-phase-approximation-amended (RPA-amended) Nilsson-Strutinskij method of calculating nuclear binding energies, the conventional shell correction terms derived from the independent-nucleon model and the Bardeen-Cooper-Schrieffer pairing theory are supplemented by a term which accounts for the pair-vibrational correlation energy. This term is derived by means of the RPA from a pairing Hamiltonian which includes a neutron-proton pairing interaction. The method was used previously in studies of the pattern of binding energies of nuclei with approximately equal numbers $N$ and $Z$ of neutrons and protons and even mass number $A = N + Z$. Here it is applied to odd-$A$ nuclei. Three sets of such nuclei are considered: (i) The sequence of nuclei with $Z = N - 1$ and $25 \le A \le 99$. (ii) The odd-$A$ isotopes of In, Sn, and Sb with $46 \le N \le 92$. (iii) The odd-$A$ isotopes of Sr, Y, Zr, Nb, and Mo with $60 \le N \le 64$. The RPA correction is found to contribute significantly to the calculated odd-even mass differences, particularly in the light nuclei. In the upper $sd$ shell this correction accounts for almost the entire odd-even mass difference for odd $Z$ and about half of it for odd $N$. The size and sign of the RPA contribution varies, which is explained qualitatively in terms of a closed expression for a smooth RPA counter term.